I am not entirely sure what you are asking...I mean, given finite time of course you can! On the other hand, there isn't a definitive answer. For example, take,
( denoting the cyclic group of order ), with your elements being of the form with . Now, let . Clearly, if then , while if then . Clearly, . On the other hand, if we let then contains but still...so, basically, it depends on and and , and can be very different depending on different choices...